### Abstract

In this expository article, we discuss some fundamentals of well-known matrix partial orders that are closely associated with space preorder on rectangularmatrices. Particularly, we consider partial order defined by space decomposition, star ordering, and minus partial order for our discussion. These relations are closelyassociated with comparison of column spaces and row spaces of matrices. Resultsassociated with selected matrix relation that are known in the literature along withsome interesting observations are put together. At many places, though the proofsof several results are known in the past literature, by part or completely, for betterreading purpose, independent proofs are provided.

Original language | English |
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Title of host publication | Combinatorial Matrix Theory and Generalized Inverses of Matrices |

Publisher | Springer India |

Pages | 195-226 |

Number of pages | 32 |

ISBN (Electronic) | 9788132210535 |

ISBN (Print) | 9788132210528 |

DOIs | |

Publication status | Published - 01-01-2013 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Combinatorial Matrix Theory and Generalized Inverses of Matrices*(pp. 195-226). Springer India. https://doi.org/10.1007/978-81-322-1053-5_17

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*Combinatorial Matrix Theory and Generalized Inverses of Matrices.*Springer India, pp. 195-226. https://doi.org/10.1007/978-81-322-1053-5_17

**Matrix partial orders associated with space preorder.** / Prasad, K. Manjunatha; Mohana, K. S.; Santhi Sheela, Y.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Matrix partial orders associated with space preorder

AU - Prasad, K. Manjunatha

AU - Mohana, K. S.

AU - Santhi Sheela, Y.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - In this expository article, we discuss some fundamentals of well-known matrix partial orders that are closely associated with space preorder on rectangularmatrices. Particularly, we consider partial order defined by space decomposition, star ordering, and minus partial order for our discussion. These relations are closelyassociated with comparison of column spaces and row spaces of matrices. Resultsassociated with selected matrix relation that are known in the literature along withsome interesting observations are put together. At many places, though the proofsof several results are known in the past literature, by part or completely, for betterreading purpose, independent proofs are provided.

AB - In this expository article, we discuss some fundamentals of well-known matrix partial orders that are closely associated with space preorder on rectangularmatrices. Particularly, we consider partial order defined by space decomposition, star ordering, and minus partial order for our discussion. These relations are closelyassociated with comparison of column spaces and row spaces of matrices. Resultsassociated with selected matrix relation that are known in the literature along withsome interesting observations are put together. At many places, though the proofsof several results are known in the past literature, by part or completely, for betterreading purpose, independent proofs are provided.

UR - http://www.scopus.com/inward/record.url?scp=84888380231&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84888380231&partnerID=8YFLogxK

U2 - 10.1007/978-81-322-1053-5_17

DO - 10.1007/978-81-322-1053-5_17

M3 - Chapter

SN - 9788132210528

SP - 195

EP - 226

BT - Combinatorial Matrix Theory and Generalized Inverses of Matrices

PB - Springer India

ER -